"You're going to have a senator that works for all West Virginians," Morrisey said in his victory speech.

President Trump has urged Republicans in the state not to vote for Blankenship, citing his inability to win the general election in November, as the GOP looks to unseat Democratic Sen. Joe Manchin. Blankenship cited Mr. Trump's tweet as perhaps the biggest factor in his loss. He came in third, behind both Morrisey and Evan Jenkins.

But West Virginia wasn't the only state with an important primary election Tuesday night. Businessman and self-described outsider Mike Braun won the GOP Senate primary in Indiana, besting Reps. Luke Messer and Todd Rokita.

Former chairman of the Consumer Financial Protection Bureau Richard Cordray won the Democratic nomination for governor in Ohio. Mike DeWine won the Republican nomination in the state for the same seat. They will face off in November.

Follow live updates from earlier:

Mark Harris upset incumbent Robert Pittenger in North Carolina

Three-term incumbent Rep. Robert Pittenger has conceded his loss in a Republican primary in North Carolina to the Rev. Mark Harris, a Baptist pastor he only narrowly beat two years ago, according to the Associated Press. Both Pittinger and Harris campaigned as evangelical Christians who would outdo the other to support President Trump, who did not endorse either candidate.

Harris will now face Democrat Dan McCready, a Marine veteran who has already raised almost $2 million.

In House District 1, Democratic incumbent G.K. Butterfield will face off against Republican Roger Allison. Both candidates were unopposed.

District 2's incumbent Republican representative George Holding won his party's primary. Former state representative Linda Coleman won the Democratic contest. They'll face Libertarian candidate Jeff Matemu in November.

In District 4, longtime Democratic representative David Price easily won his primary. Barbara Howe won the Libertarian primary. In November, they'll face Republican Steve Von Loor.

In District 6, Ryan Watts won the Democratic primary. In November, he will face incumbent Mark Walker, who did not face a Republican challenger.

In the 7th district, Democrat Kyle Horton won his party's contest. He'll be up against Republican incumbent David Rouzer in the general election.

In the 8th district, Democrat Frank McNeill a former mayor of Aberdeen, won the Democratic primary and will move on to face Republican representative Richard Hudson.

Morrisey gives victory speech

Morrisey's victory speech gave a preview for what the general election might look like.

Morrisey said the general election won't be one filled with personal attacks, but claimed Manchin has become a creature of Washington.

"You're going to have a senator that works for all West Virginians," Morrisey told his supporters.

But that doesn't mean things will be easy for Morrisey in the fall. He and his family moved to West Virginia in 2006, and was born in New York City.

Vice President Mike Pence congratulated Morrisey on Twitter.

Congratulations to @MorriseyWV on his victory tonight. @RealDonaldTrump and I look forward to working with him. The great people of WV need a senator who supports the #MAGA agenda.

McConnell trolls Blankenship

Mitch McConnell -- whom Blankenship has called "Cocaine Mitch" -- trolled Blankenship after his loss became clear. McConnell, in an image of him surrounded by White powder, tweeted, "Thanks for playing, @DonBlankenship."

The image of McConnell is essentially the same one used by Netflix to promote "Narcos," a show about Colombian drug lord Pablo Escobar.

Blankenship tells supporters: "Don't feel sorry for me"

Blankenship took a moment to -- seemingly -- concede, acknowledging that he believes he has lost.

Blankenship attributed his loss, perhaps more than anything, to Mr. Trump's tweet urging people not to vote for him earlier this week. He also thanked supporters, and the media. Blankenship said he'll now have more time for his family and traveling to places like Paris.

"Don't feel sorry for me," Blankenship said.

Blankenship reflected on the opportunities he, as the child of a single mother, had growing up, mentioning a time he says he visited the White House.

"I learned more in the poor house and the big house than I learned in the other houses," he said.

Republican Jim Renacci performing well in Ohio Senate race

With more than 500,000 votes cast among Republicans, Jim Renacci is clearly leading. He has nearly 46 percent of the vote compared with the next GOP candidate, Mike Gibbons. Renacci is a current congressman in the state.

If Renacci wins, he will face off against Democratic Sen. Sherrod Brown.

Richard Cordray, Mike DeWine expected to take party nominations in Ohio governor's race

Richard Cordray, the former head of the Consumer Financial Protection Bureau (CFPB) is expected to win the race for the Democratic nomination for governor in Ohio.

Mike DeWine is expected to win the Republican nomination for governor. The two are expected to face off in November.

Cordray tweeted his appreciation.

My thanks to the people of Ohio. This victory happened for a reason. You demanded changed and we heard you. We want the same.

Richard Cordray way ahead in Ohio governor's race

Richard Cordray, the former head of the Consumer Financial Protection Bureau (CFPB), is outpacing his most serious contender in the Democratic bid to win the nomination for the governor's race. With more than 180,000 votes in, Cordray has nearly 63 percent of the vote, compared with Dennis John Kucinich's nearly 23 percent.

Mike Braun holds strong performance in Indiana

With more than 100,000 votes in, businessman Mike Braun appears to be easily pulling ahead of Reps. Luke Messer and Todd Rokita. At 8:32 p.m., according to the Indiana state government, Braun had 42.2 percent of the vote.

CBS News' Anthony Salvanto breaks down West Virginia

Republican voters want a candidate who is like Trump, explains CBS News' Elections and Surveys Director Anthony Salvanto. Watch him break down what that looks like for Tuesday night's races.

First results arrive in West Virginia

Votes are -- barely -- starting to roll in for West Virginia's much-anticipated Senate race. With just a few thousand votes, it's Patrick Morrisey in the lead, followed by Evan Jenkins, followed by Don Blankenship with just 16.5 percent of the vote. But the night is young.

Mike Braun pulls ahead of competitors in Indiana

Initial results, with just more than 19,000 ballots case, according to the Indiana state government, Mike Braun is pulling easily ahead of his contenders, Todd Rokita and Luke Messer. Braun, a businessman, has cast himself as a conservative outsider who isn't a part of the Washington, D.C. system.

No results yet in West Virginia

There are still no precincts reporting in West Virginia, and won't be for a short while. Some results are expected by 8 p.m.

Blankenship tweeted this out shortly before polls closed.

If you haven't voted yet, the polls are open for just under one more hour. I'll be at the Marriott in downtown Charleston tonight watching results as they come in with my family, friends and supporters. #WVSenpic.twitter.com/NTGKHDtL1o

Mike Pence's brother pulls ahead in Indiana

It's early, but Greg Pence, the brother of Vice President Mike Pence, is pulling ahead of his main opponent, Jonathan Lamb. If he wins, the Pence brother will hold the same seat that his brother did for nearly a decade.

Polls now closed in Indiana, West Virginia, Ohio and North Carolina

As of 7:30 p.m. EDT, polls are closed in all four states with major primaries Tuesday night. CBS News will deliver initial results as soon as they become available.

Polls close in Indiana

GOP chairwoman says RNC will support whoever supports Trump in West Virginia

GOP Chairwoman Ronna McDaniel told Fox News' Neil Cavuto the Republican National Committee will support the Republican candidate who supports the president's agenda, when asked whether the RNC will back Blankenship if he wins Tuesday night.

"Yeah I'm going to support people who support the president's agenda," McDaniel said. "I love these May primaries because it allows us to find who are nominees are going to be and coalesce around them ... the most important message coming out of today in all these states after these candidates have had these competitive primaries, come together."

Polls closing first in Indiana

Indiana is divided into Central and Eastern time zones. But Indiana's polls are the first to close, at 7 p.m. EDT.

Results won't be immediate, however. They will take some time to trickle in.

Other races to watch

But while the West Virginia race is getting the most attention, that isn't the only primary that matters.

Republicans in Indiana also face a bitter Senate primary, as they look to upset another vulnerable Democrat -- Sen. Joe Donnelly. Congressmen Luke Messer and Todd Rokita face off against former state representative Mike Braun, who calls his opponents "swamp creatures."

Then there's Ohio, where Democrats and Republicans have their own primaries to see what a November matchup to replace Gov. John Kasich will look like.